Infrared QCD

8 nov. 2017 à 08:30
→
10 nov. 2017 à 15:30
Europe/Paris

483A - Malevitch (APC)

483A - Malevitch

APC

University Paris Diderot

Description

The workshop aims at bringing together experts in the field of infrared aspects of Yang-Mills theories and QCD, in particular, in the context of (Landau gauge) correlation functions, both in the vacuum and at finite temperature and density. State of the art calculations employing various (lattice and continuum) approaches as well as crucial open issues concerning, e.g., the dynamical generation of a gluon mass, or the phase diagram and thermodynamics of QCD will be critically discussed.

Results for Yang-Mills vacuum correlation functions in the Landau gauge from equations of motion (45+15)1h

Recent results for Yang-Mills correlation functions in the Landau gauge from equations of motion of 1PI and 3PI effective actions are reviewed. The status of the truncation dependence is discussed on the basis of results for nonprimitively divergent correlation functions and for the three-dimensional case. Special emphasis is put on the renormalization of the underlying equations and perturbative resummation.

I will review the covariant variational approach to Yang-Mills theory in Landau gauge and compare it with the Hamiltonian approach. First I will treat the vacum sector. Then I will study the deconfinement phase transition by calculating the Polyakov loop potential.

Taming Gribov copies via the horizon restriction: done and to do (50+10)1h

A possible way to deal with (small) Gribov copies in the Landau gauge is to restrict the domain of integration of the gauge field variables. Such pioneering work was carried out by Gribov himself at leading order, and improved upon to all orders by Zwanziger, an effort culminating in an effective GZ action with dynamical mass scale. We briefly review this construction, using the inverse ghost propagator as “diagnostic tool” and we mention some underlying assumptions.

A major shortcoming of the original effective action was the incompatibility with BRST invariance. Recent insights allowed to reformulate it into a BRST symmetric version, thereby also opening the road to generalizing the Gribov-Zwanziger approach to other classes of gauges. We pay particular attention to the linear covariant gauge.

We discuss how dynamical effects can alter the action, resulting in the formation of (BRST invariant) d=2 condensates. A shortcoming of the current approach is that these dynamical mass scales are for now obtained by fitting to lattice data, and we propose a strategy to search for self-consistent gap equations. It remains to be seen whether such scales will be only qualitatively, or also quantitatively compatible with lattice data.

At last, we briefly turn to the finite T extension when the Polyakov loop is added to the model via a temporal background gauge field (see other talks). We discuss and illustrate how previous work (using the GZ original action) is at odds with background gauge invariance, a fact under current remediation as this can be related to the lack of BRST invariance. Though, even this improvement leaves important challenges, also present in other approaches (see also other talks).

Extracting infrared properties of QCD from the Curci-Ferrari model (45)45m

It is often believed that the infrared regime of QCD is nonperturbative. This is partly based on the fact that standard perturbation theory predicts a coupling constant which diverges at a finite (infrared) momentum scale. However lattice simmulations show no clue of such a behavior. Instead, the coupling constant is found to be bounded by a constant of order 1, which could be dealt with in perturbation theory. We review on a phenomenological approach which consists in adding to the standard Faddeev-Popov action a gluon mass (this model was introduced by Curci and Ferrari in the 70's). The model has good properties in the infrared regim and the coupling constant remains finite down to arbitrary small momentum scale, as seen in lattice simulations. We review on the systematic comparison that was performed between the 1-loop calculation in this model and lattice simulation. We finally discuss on possible origins for the gluon mass

Analytical study of Yang-Mills theory from first principles by a massive expansion (45+15)1h

Pure Yang-Mills theory is studied by perturbation theory, using an unconventional expansion with a massive free-particle gluon propagator. The exact Faddev-Popov Lagrangian is considered in a generic linear covariant gauge. The Gaussian effective potential is shown to be gauge invariant and minimal at a massive vacuum, providing a variational argument for mass generation. Loop expanding around the optimal massive vacuum, a massive expansion is recovered, yielding dressed propagators that are in very good agreement with the data of lattice simulations in the Landau gauge. No spurious counterterms or parameters are required since all the mass divergences are canceled exactly in the expansion. At one loop, the propagators are analytic functions and can be easily continued to the whole complex plane, predicting the existence of complex poles for the gluon. Because of the finite damping rate, the gluon is canceled from the asymptotic states, yielding a microscopic proof of confinement.

At finite temperature, the same variational argument provides an optimal mass that depends on temperature. A weak first order transition is observed at T_c=255 MeV where the optimal mass is discontinuous. The equation of state is studied and found in good quantitative agreement with the lattice data, from first principles and without any free parameter. The poles of the gluon propagator are studied as functions of temperature and a crossover scenario is found, with a short intrinsic lifetime of the quasi-gluon below T_c and an almost linear damping rate above T_c, as expected by standard perturbation theory in the high temperature limit.

Some applications of Renormalization Group Optimized perturbation at zero and finite temperature (45+15)1h

I will illustrate how the recently developed renormalization group optimized perturbation theory (RGOPT) resums perturbative expansions in vacuum or thermal field theories. For zero temperature QCD typically, it gives realistic approximations of the order parameters of chiral symmetry breaking (quark condensate etc). In thermal theories the convergence and scale dependence of RGOPT thermodynamical quantities are drastically improved as compared to standard perturbative expansions, and it cures the odd drastic scale dependence observed in other related methods such as the screened perturbation or (resummed) hard-thermal-loop (HTL) perturbation. I will present some recent results in scalar models, and first applications to HTL resummation for QCD thermodynamical quantities, also explaining the additionnal calculations needed in gauge theories with respect to standard HTLpt within our framework.

The computation of the pure gauge Landau gauge gluon propagator is revisited both at zero and finite temperature. For the zero temperature case we discuss the compatibility of the generalised Gribov-Zwanziger predictions and particular attention is given to the computation of the propagator for temperatures near the deconfinement phase transition. Preliminary results for the gluon of the spectral function are also discussed.

The massive Landau-de-Witt gauge at finite temperature and density (45+15)1h

We review recent results of the massive Landau-de-Witt gauge approach to the description of Yang-Mills and QCD theories at finite temperature and/or densities. In particular we consider the formal but interesting limit of heavy quarks and compare with other approaches, including the lattice as a benchmark. We also discuss some of the limitations of the method and draw some parallels with other approaches.

Lattice simulations show that the running coupling constants obtained through QCD vertices differ in the infrared even though their bare values coincide. For instance, at low momenta the strength of the quark-gluon coupling is about twice the ghost-gluon coupling. None of them diverge in the infrared as it is predicted by standard perturbation theory. Moreover, the ghost-gluon coupling remains moderate even in the infrared. This observation motivates the use of perturbation theory in the ghost-gluon sector in the frame of a massive deformation of QCD Lagrangian in Landau gauge. However, perturbation theory in the quark sector within this massive Lagrangian doesn´t bring as good results as in the pure Yang-Mills case, as should be expected from the larger value of the quark-gluon coupling constant.
We propose a controlled systematic expansion in full QCD based in two small parameters: first the Yang.Mills sector couplings and second the inverse of the number of colors (large-Nc limit). The second approximation relies on the fact that the general features of QCD can be observed in the large-Nc limit. This systematic expansion allows us to properly introduce the use of the renormalization group for the rainbow resummation.
At leading order, this double expansion leads to the well-known rainbow approximation for the quark propagator whose solution shows spontaneous chiral symmetry breaking for sufficiently large quark-gluon coupling constant.

Polyakov-loop potentials for the phenomenological investigation of the QCD phase structure (45+15)1h

Polyakov-loop-extended chiral models are useful to get a glimpse on the phase structure of strongly-interacting matter. However, these models rely on simple parameterisations of the Polyakov-loop potential and with present parameter sets different parameterisations give results for pure gauge theory that differ considerably. Of course this introduces even larger uncertainties when the potential is coupled to quarks in Polyakov-loop-extended chiral models. Therefore, it is important to find parameter sets for the different parameterisations such that they agree in their description of latest lattice data on Yang-Mills theory. Furthermore, these parametrised Polyakov-loop potentials miss so far any information on the slope of the potential away from its minimum. But this is the area which determines the expectation value of the Polyakov loop in Polyakov-loop--extended chiral models. Hence, we suggest to include to the existing parameterisations information about the global shape of the Polyakov-loop potential from calculations in nonperturbative, continuum approaches. We show how the existing parametrised Polyakov-loop potentials differ from the calculated ones and which information of the calculated potentials could be included to the parameterisations to increase the predictability of the phase structure of QCD with Polyakov-loop--extended chiral models.